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subject to
Later in this section we shall show how to solve this type of mathematical problem geometrically.
EXAMPLE 2 Maximizing Annual Yield
A woman has up to $10,000 to invest. Her broker suggests investing in two bonds, A and B. Bond A is a rather risky bond with an
annual yield of 10%, and bond B is a rather safe bond with an annual yield of 7%. After some consideration, she decides to invest
at most $6000 in bond A, to invest at least $2000 in bond B, and to invest at least as much in bond A as in bond B. How should she
invest her $10,000 in order to maximize her annual yield?
Solution
To formulate this problem mathematically, let be the number of dollars to be invested in bond A, and let be the number of
dollars to be invested in bond B. Since each dollar invested in bond A earns $.10 per year and each dollar invested in bond B earns
$.07 per year, the total dollar amount z earned each year by both bonds is
The constraints imposed can be formulated mathematically as follows:
Invest no more than $10,000:
Invest at most $6000 in bond A:
Invest at least $2000 in bond B:
Invest at least as much in bond A as in bond B:
We also have the implicit assumption that and are nonnegative:
Thus the complete mathematical formulation of the problem is as follows: Find values of and that maximize
subject to
EXAMPLE 3 Minimizing Cost
